REWARD: Is there a word for this?

No.

so I used the online make the library look stuff up thing and one of the definitions of aligator is a. U.S. slang. A non-playing devotee of swing music, a hep-cat. (No longer in use.)
so it seems that maybe a word meaning having to do with aligators might be Jazz afficianato

so I used the online make the library look stuff up thing and one of the definitions of aligator is a. U.S. slang. A non-playing devotee of swing music, a hep-cat. (No longer in use.)
so it seems that maybe a word meaning having to do with aligators might be Jazz afficianato

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Alligatoring.

Gatoriffic.

Crocodiculous.

How about Lagartian.

The name alligator is an anglicized form of the Spanish el lagarto ("the lizard"), the name by which early Spanish explorers and settlers in Florida called the alligator

I think anybody who'd ask this question is a fag so I guess the best word to describe having to do with alligators is faggotry

now give me a prize

I think we have a winner.

Such a terribly hard try at being droll gets its humor from the premise that there would be no such word. However, there is.

The adjective for having to do with alligators is the same as the one for crocodiles: crocodilian.

Crocodilian is correct, and I think it's sad that someone who made it through high school couldn't figure that out on his own.

alligatorial, alligatory, alligatious, alligateful, or alligative are all acceptable.

gatoresque

Allegory